Topological spaces in which Blumberg’s theorem holds

Autor:	H. E. White
Rok vydání:	1974
Předmět:	Topological manifold Discrete mathematics Pure mathematics Fundamental group Topological algebra Applied Mathematics General Mathematics MathematicsofComputing_GENERAL Hausdorff space Topological space Topological vector space T1 space Locally convex topological vector space Mathematics
Zdroj:	Proceedings of the American Mathematical Society. 44:454-462
ISSN:	1088-6826 0002-9939
DOI:	10.1090/s0002-9939-1974-0341379-3
Popis:	H. Blumberg proved that, if f f is a real-valued function defined on the real line R R , then there is a dense subset D D of R R such that f | D f|D is continuous. J. C. Bradford and C. Goffman showed [3] that this theorem holds for a metric space X X if and only if X X is a Baire space. In the present paper, we show that Blumberg’s theorem holds for a topological space X X having a σ \sigma -disjoint pseudo-base if and only if X X is a Baire space. Then we identify some classes of topological spaces which have σ \sigma -disjoint pseudo-bases. Also, we show that a certain class of locally compact, Hausdorff spaces satisfies Blumberg’s theorem. Finally, we describe two Baire spaces for which Blumberg’s theorem does not hold. One is completely regular, Hausdorff, cocompact, strongly α \alpha -favorable, and pseudo-complete; the other is regular and hereditarily Lindelöf.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::8ffaf217429b1b3e3072acc73a10b751 https://doi.org/10.1090/s0002-9939-1974-0341379-3 Zobrazit plný text záznamu